Engineering Calculation Tools
This tool calculates the heat flux a panel is actually running at, from the flow rate and inlet/outlet temperature measured on the panel circuit. If panel geometry is entered, it also checks local boiling risk and fire-side surface temperature.
This calculator was built for water-cooled panels; the same method also applies to copper panels and water-cooled ducts.
Panel drawing to hand? Add the geometry and the tool will check for local boiling and fire-side overheating.
Heat Flux
150.9 kW/m²
Heat Load: 452.8 kW · Specific Flow: 10 m³/(h·m²)
This calculation is an approximate starting value based on the formulas in Toulouevski & Zinurov, "Innovation in Electric Arc Furnaces", 2nd ed., Chapter 12. Arc coverage and slag thickness change continuously through a heat, so any single measurement is only a snapshot. For an exact design, talk to DNL's engineers.
Measured flow and temperature rise give the heat removed; divided by projected area, that's the heat flux. Channel geometry and flow give the water velocity, velocity gives the convective coefficient via Toulouevski & Zinurov formula (3.36), and that gives the water-side wall temperature t₂.
If t₂ exceeds the boiling point at the circuit pressure, vapour forms on the wall. Toulouevski & Zinurov are explicit that this mode must be avoided: in poorly flushed corners, bubble boiling can alternate with film boiling, and a stable vapour film insulates the wall and burns through it. That is why the circuit pressure is an input.
Conduction through the wall gives t₁. Above roughly 300°C for copper and 400°C for low-carbon steel, wear accelerates and burn-back can follow in a short period.
Thermal conductivity varies enough with temperature to matter: low-carbon steel is 0.0556 kW/(m·K) at 100°C and 0.0450 at 400°C, a 19% swing. Reading it only at the cold boundary understates the resistance and so understates t₁ — it would make the margin look larger than it is. The tool follows Toulouevski & Zinurov's own two-pass method: lambda at t₂ gives a provisional t₁, then lambda at the mean wall temperature gives the reported value.
A measurement over any period yields an average. Toulouevski & Zinurov require elements to be designed for peak flux, which acts briefly but recurs and is what determines durability. This tool reports an average and cannot convert it to a peak.
Panel service life, material and thickness selection, hot-spot location, scale deposit effects, complex geometry — these all change the answer, and no published formula covers them from measurement alone. Talk to DNL's engineers for a project-specific assessment.
Take a panel circuit with a 3 m² projected area, 30 m³/h flow, heating from 35°C to 48°C, a 60 mm ID round channel with 2 parallel circuits, running at 4 bar absolute, with a 10 mm low-carbon steel wall (K = 1).
This example shows a healthy circuit running with a wide margin on both criteria — a useful reference for what "fine" looks like before troubleshooting a marginal one.
Peak design values selected from Toulouevski, Y.N. & Zinurov, I.Y., "Innovation in Electric Arc Furnaces", 2nd ed., Springer Berlin Heidelberg, 2013, Chapter 12, Table 12.2, p. 220. Design must use peak, not time-averaged, flux.
| Element and Operating Condition | Peak Flux (kW/m²) |
|---|---|
| Wall and roof panels | 600–700 |
| Heavily encrusted panels | 200–300 |
See the source for the complete table and its experimental basis.
DNL's note: these are peak design values — it's normal for the average flux you measure to come out lower. Once slag crust builds up on the panel, the peak value drops to 200-300 kW/m².
The water boiling point at the circuit pressure — the value the whole boiling check is measured against.
| Pressure (bar abs) | Boiling Point (°C) |
|---|---|
| 1 | 99.5 |
| 2 | 120.4 |
| 3 | 133.7 |
| 4 | 143.7 |
| 5 | 151.9 |
| 6 | 158.9 |
| 7 | 165.1 |
| 8 | 170.5 |
| 9 | 175.4 |
| 10 | 179.9 |
Toulouevski, Y.N. & Zinurov, I.Y., "Innovation in Electric Arc Furnaces", 2nd ed., Springer Berlin Heidelberg, 2013, Ch. 12, §12.2, p. 217 — above these limits, wear accelerates and burn-back can follow in a short period.
| Material | Limit (°C) |
|---|---|
| Copper | 300 |
| Steel | 400 |
It's calculated from the measured flow and inlet/outlet temperature on your panel circuit. For the worked example on this page, that comes to 150.9 kW/m² — not an estimate, but a heat flux derived from the panel's actual operating data.
Local boiling is present when the water-side wall temperature (t₂) exceeds the boiling temperature at the circuit pressure (t_S). Pressure matters because the boiling point rises with it — the same circuit at the same temperature can be safe at one pressure and boiling at a lower one.
According to Toulouevski, Y.N. & Zinurov, I.Y., "Innovation in Electric Arc Furnaces", 2nd ed., Springer Berlin Heidelberg, 2013, Ch. 12, §12.2, p. 217, roughly 400°C for low-carbon steel and 300°C for copper. Above these limits, wear accelerates and burn-back can follow in a short period.
Because what you measured is an average, while the published Table 12.2 figures are peak design values. Peak flux is brief but recurring, and it's what determines durability — the average can look low even when the peaks run much higher. This tool cannot convert an average into a peak.
Yes. According to Toulouevski & Zinurov, peak flux drops to 200–300 kW/m² on heavily encrusted panels. This tool measures whatever state the panel is in at that moment — since slag build-up changes over time, the same panel will give different results at different times.
